2023/05/15 by Yan Zhuang, Zhuang, Yan, Daxiong Piao +3
Materials Science · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Liquid Crystal Research Advancements #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2305.08368
openalex publication_date 2023/05/15 · openalex created_date 2023/05/17 · openalex updated_date 2026/07/28
We consider the existence of invariant curves of real analytic reversible mappings which are quasi-periodic in the angle variables. By the normal form theorem, we prove that under some assumptions, the original mapping is changed into its linear part via an analytic convergent transformation, so that invariants curves are obtained. In the iterative process, by solving the modified homological equations, we ensure that the transformed mapping is still reversible. As an application, we investigate the invariant curves of a class of nonlinear resonant oscillators, with the Birkhoff constants of the corresponding Poincar\acutee mapping all zeros or not.